# How do you simplify the square root of 125/80?

Sep 20, 2015

$\sqrt{\frac{125}{80}} = \frac{5}{4}$
If $a \ge 0$ then $\sqrt{{a}^{2}} = a$
$\sqrt{\frac{125}{80}} = \sqrt{\frac{5 \times 25}{5 \times 16}} = \sqrt{\frac{25}{16}} = \sqrt{{5}^{2} / {4}^{2}} = \sqrt{{\left(\frac{5}{4}\right)}^{2}} = \frac{5}{4}$